﻿ Step 11.1: Piggyback Sliders as XY Table

# Step 11.1: Piggyback Sliders as XY Table

The Piggyback Slider configuration is two Sliders:

 • Slider[A] : moves along the X-axis† of the Mechanism-Plane
 • Slider[B] :  mounted to Slider[A], and moves along the Y-axis† of the Slider[A]

The Piggyback Slider Configuration is only one way to model an XY-Path.

You can also use a Motion-Path.

The Sliders do not need to be in the X-axis and Y-axis directions or even it right-angles to each other. We describe them in these directions for convenience only.

For example, they may be in the Radial and Tangential direction relative to a radius line of a circle.

#### Mechanical Systems that follow the 'XY'-Path:

Linear-Slides (Slide-ways + Slide-blocks)

 o The Piggyback Sliders are modelled in the same way as the Linear-Motion Technology' [the motors and the mechanics].
 o The motors that drive the 'Sliders' have the same nominal* motion as the Piggyback Sliders. See Step 11.1

* For example, a motor may rotate a Pulley to move a Belt, or a Ball-Screw to move a Nut. In each case, the motors rotate a different number of rotations, but their rotation is a linear relationship to the Slider's motion.

 a. Use linear-slides to design an XY-table.
 b. Connect Dyads between the slide-blocks and the machine-frame.
 c. Use cams or servomotors on the Machine Frame to drive the Dyads and thus the XY-table

Design and add motions to the XY-table directly. MechDesigner will use inverse-kinematics to calculate the motions for the cam-followers or servomotors - See Step 11.2

Translating Beam [a Part that moves on the Mechanism-Plane but does not rotate]

 o It is possible to configure a translating-beam that does not need linear-slides.
 o Look at this video. This example happens to show 3 independent axes to control the motion of a Beam. In this case the motion of the beam can be specified to translate or rotate.
 o Use Piggyback Sliders to specify the XY-Path, even though they are not in the mechanical system. See Step 11.3.
 Technical Note: Rectilinear Translation: All points in a Part have the same and parallel motions. Curvilinear Translation: All points in a Part have the same, but not necessarily straight, motions.

#### Quick Instructions: Add Piggyback Sliders Quick Instructions:

 STEP 1. Add a X-Slider to a horizontal Line in the Base-Part
 STEP 2. Edit the X-Slider. Add a Line that is parallel to the Y-axis
 STEP 3. Add the Y-Slider to the Line that is parallel to the Y-axis of X-Slider.
 STEP 4. Design the motions for each Slider.
 STEP 5. Add a Trace-Point to a Point that moves with the Y-Slider.
 STEP 6. Run menu  > Cycle to watch the kinematic-chain move.

#### 'Detailed Instructions: Add Piggyback Sliders' STEP 1. Edit the Base-Part; Add a Horizontal Line; Close the Part-Editor
 STEP 2. Add a Part; Add a Slide-Joint between the Part and the Line in the Base-Part
 STEP 3. Add a Motion-Dimension FB to identify the X Slider
 STEP 4. Add a Linear-Motion FB and a Motion FB to the graphic-area
 STEP 5. Connect the FBs
 STEP 6. Rename the Slider Part to 'X SLIDER' Edit the X-Slider, Add a Vertical Line

 STEP 1. Edit the length of the X-Slider Part
 STEP 2. I have changed it to 100mm.
 STEP 4. Add a Vertical Constraint to the Line
 STEP 5. Dimension and add Constraints to fully specify the Line
 STEP 6. The length of the new Line is 100mm. The Origin of the new Line is 'Coincident' with the Origin of the Part.
 STEP 7. Close the Part-Editor STEP 1. Add a Part; Add a Slide-Joint between the new Part and the vertical Line in the X-Slider
 STEP 2. Add a Motion-Dimension FB to specify the Position of the Y-Slider.
 STEP 3. Add a Linear-Motion FB and a Motion FB to the graphic-area
 STEP 4. Connect the FBs
 STEP 5. Rename the new Slider Part to 'Y-SLIDER' Get Motions for the Sliders

 STEP 1. Double-click the Motion FB connected to the X-Slider
 STEP 2. Click the Motion for the X-Slider
 STEP 3. Double-click the Motion FB connected to the Y-Slider
 STEP 4. Click the Motion for the Y-Slider
 STEP 5. Show the Path traced out by the Y-Slider
 STEP 6. Use Add Trace-Point in the Kinematic-elements toolbar to add a Trace-Point to a Point in the Y-Slider STEP 7: Run menu > Cycle, [or use] [C]

X Motion

This is a Motion for the X-axis.

Use a Motion FB to link this motion to the Motion-Dimension FB to move the X-Slider. Y Motion

This is a Motion for the Y-axis.

Use a different Motion FB to link to the Motion-Dimension FB to move the Y-Slider.

These two example motions define an XY motion path on the Mechanism-Plane

We can show the XY motion path in the graphic-area with a Trace-Point.

### Degrees-of-Freedom of Piggyback Sliders 'Degrees-of-Freedom' and 'Mobility' of Piggyback Sliders

The kinematic elements in a Piggyback Slider kinematic-chain:

 • two 'added Parts' (with the BasePart, there are three Parts in total)
 • two Joints.

Gruebler Equation to find the number of Degrees-of-Freedom (F):

F = 3(P-1) – 2J  : P = Number of Parts ; J = Number of Joints

F = 3*(3-1) – 2*2

F = 6 – 4 = 2

Mobility = # Degrees-of-Freedom(F) – # Motion-Dimensions = 2 – 2 = 0.

### Kinematics Tree of Piggyback Sliders Kinematics-Tree for Piggyback Sliders.

There is:

 • One kinematic-chain [Solved Mechanisms]

The Solved Mechanism has:

 • Two Sliders

### Machines that use Piggyback Sliders

Example machines include:

 • Pen Plotters
 • Water-Jet Cutters
 • Laser Markers or Cutters An XY 'Gantry' Robot

Imagine a 'Pen Plotter'. Look at the video to the left.

This 'Plotter' moves a Pen along a slide, say the Y-axis slide. The X-axis carries the Y-axis slide.  The combined movement plots the drawing.

With this machine, there is an EXACT link between a Point at position X1,Y1 and the control positions of the slider motors. The system is Kinematically Linear.

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